The solution to a system of equations is \( (5,-19) \). Select the two equations that could make up the system. \( \square \begin{array}{l}y=-7 x+16 \\ \square \\ \square=-3 x-6 \\ y=-2 x-9 \\ \square \\ y=-x-17 \\ y=2 x-23\end{array} \)

To determine which two equations from the list have the solution \( (5, -19) \), we'll substitute \( x = 5 \) and \( y = -19 \) into each equation to see which ones are satisfied. 1. **\( y = -7x + 16 \)** \[ -19 = -7(5) + 16 \\ -19 = -35 + 16 \\ -19 = -19 \quad \text{✓} \] This equation is satisfied by \( (5, -19) \). 2. **\( y = -3x - 6 \)** \[ -19 = -3(5) - 6 \\ -19 = -15 - 6 \\ -19 = -21 \quad \text{✗} \] This equation is **not** satisfied by \( (5, -19) \). 3. **\( y = -2x - 9 \)** \[ -19 = -2(5) - 9 \\ -19 = -10 - 9 \\ -19 = -19 \quad \text{✓} \] This equation is satisfied by \( (5, -19) \). 4. **\( y = -x - 17 \)** \[ -19 = -5 - 17 \\ -19 = -22 \quad \text{✗} \] This equation is **not** satisfied by \( (5, -19) \). 5. **\( y = 2x - 23 \)** \[ -19 = 2(5) - 23 \\ -19 = 10 - 23 \\ -19 = -13 \quad \text{✗} \] This equation is **not** satisfied by \( (5, -19) \). **Conclusion:** The two equations that are satisfied by \( (5, -19) \) are: \[ \boxed{\begin{aligned} y &= -7x + 16 \\ y &= -2x - 9 \end{aligned}} \]